Analytic calculations of MHD equilibria and of MHD stability boundaries in fusion plasmas

In this work, two separate aspects of ideal MHD theory are considered. In the first part, analytic solutions to the Grad-Shafranov equation (GSE) are presented, for two families of source functions: functions which are linear in the flux function T , and functions which are quadratic in T. The solutions are both simple and very versatile, since they describe equilibria in standard tokamaks, spherical tokamaks, spheromaks, and field reversed configurations. They allow arbitrary aspect ratio, elongation, and triangularity as well as a plasma surface that can be smooth or possess a double or single null divertor X-point. The solutions can also be used to evaluate the equilibrium beta limit in a tokamak and spherical tokamak in which a separatrix moves onto the inner surface of the plasma. In the second part, the reliability of the ideal MHD energy principle in fusion grade plasmas is assessed. Six models are introduced, which are constructed to better describe plasma collisonality regimes for which the approximations of ideal MHD are not justified. General 3-D quadratic energy relations are derived for each of these six models, and compared with the ideal MHD energy principle. Stability comparison theorems are presented. The main conclusion can be summarized in two points. (1) In systems with ergodic magnetic field lines, ideal MHD accurately predicts marginal stability, even in fusion grade plasmas. (2) In closed field line geometries, however, the ideal MHD predictions must be modified. Indeed, it is found that in collisionless plasmas, the marginal stability condition for MHD modes is inherently incompressible for ion distribution functions that depend only on total energy. The absence of compressibility stabilization is then due to wave particle resonances. An illustration of the vanishing of plasma compressibility stabilization in closed line systems is given by studying the particular case of the hard-core Z-pinch.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Nuclear Science and Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2010

Author dc:creator

• Cerfon, Antoine Julien

Advisor dc:contributor.advisor

• Jeffrey P. Freidberg.

• Nuclear Science and Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/76494

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/76494